Fluctuations of Young diagrams for symplectic groups
Organizers
Speaker
Time
Friday, January 24, 2025 1:00 PM - 2:30 PM
Venue
A14-201
Online
Zoom 242 742 6089
(BIMSA)
Abstract
Consider an matrix of i.i.d. Bernoulli random numbers with some value of . Dual RSK algorithm gives a bijection of this matrix to a pair of Young tableaux of conjugate shape, which is manifestation of skew Howe -duality. Thus the probability measure on zero-ones matrix leads to the probability measure on Young diagrams proportional to the ratio of the dimension of -representation and the dimension of the exterior algebra . Similarly, by applying Proctor's algorithm based on Berele's modification of the Schensted insertion, we get skew Howe duality for the pairs of groups . In the limit when , -case is relatively easily studied by use of free-fermionic representation for the correlation kernel. But for the symplectic groups there is no convenient free-fermionic representation. We use Christoffel transformation to obtain the semiclassical orthogonal polynomials for .